Space-time Autoregressive Integrated Moving Average Research Articles

A Unified Spatio-Temporal Model for Short-Term Traffic Flow Prediction

This paper proposes a unified spatio-temporal model for short-term road traffic prediction. The contributions of this paper are as follows. First, we develop a physically intuitive approach to traffic prediction that captures the time-varying spatio-temporal correlation between traffic at different measurement points. The spatio-temporal correlation is affected by the road network topology, time-varying speed, and time-varying trip distribution. Distinctly different from previous black-box approaches to road traffic modeling and prediction, parameters of the proposed approach have physically intuitive meanings which make them readily amendable to suit changing road and traffic conditions. Second, unlike some existing techniques that capture the variation of spatio-temporal correlation by a complete re-design and calibration of the model, the proposed approach uses a unified model that incorporates the physical factors potentially affecting the variation of spatio-temporal correlation into a series of parameters. These parameters are relatively easy to control and adjust when road and traffic conditions change, thereby greatly reducing the computational complexity. Experiments using two sets of real traffic traces demonstrate that the proposed approach has superior accuracy compared with the widely used space–time autoregressive integrated moving average (STARIMA) and the back propagation neural network approaches, and is only marginally inferior to that obtained by constructing multiple STARIMA models for different times of the day, however, with a much reduced computational and implementation complexity.

Passenger Flow Prediction of Urban Rail Transit Based on Deep Learning Methods

The rapid development of urban rail transit brings high efficiency and convenience. At the same time, the increasing passenger flow also remarkably increases the risk of emergencies such as passenger stampedes. The accurate and real-time prediction of dynamic passenger flow is of great significance to the daily operation safety management, emergency prevention, and dispatch of urban rail transit systems. Two deep learning neural networks, a long short-term memory neural network (LSTM NN) and a convolutional neural network (CNN), were used to predict an urban rail transit passenger flow time series and spatiotemporal series, respectively. The experiments were carried out through the passenger flow of Beijing metro stations and lines, and the prediction results of the deep learning methods were compared with several traditional linear models including autoregressive integrated moving average (ARIMA), seasonal autoregressive integrated moving average (SARIMA), and space–time autoregressive integrated moving average (STARIMA). It was shown that the LSTM NN and CNN could better capture the time or spatiotemporal features of the urban rail transit passenger flow and obtain accurate results for the long-term and short-term prediction of passenger flow. The deep learning methods also have strong data adaptability and robustness, and they are more ideal for predicting the passenger flow of stations during peaks and the passenger flow of lines during holidays.

A new Seasonal Difference Space-Time Autoregressive Integrated Moving Average (SD-STARIMA) model and spatiotemporal trend prediction analysis for Hemorrhagic Fever with Renal Syndrome (HFRS).

Hemorrhagic fever with renal syndrome (HFRS) is a naturally-occurring, fecally transmitted disease caused by a Hantavirus (HV). It is extremely damaging to human health and results in many deaths annually, especially in Hubei Province, China. One of the primary characteristics of HFRS is the spatiotemporal heterogeneity of its occurrence, with notable seasonal differences. In view of this heterogeneity, the present study suggests that there is a need to focus on trend simulation and the spatiotemporal prediction of HFRS outbreaks. To facilitate this, we constructed a new Seasonal Difference Space-Time Autoregressive Integrated Moving Average (SD-STARIMA) model. The SD-STARIMA model is based on the spatial and temporal characteristics of the Space-Time Autoregressive Integrated Moving Average (STARMA) model first developed by Cliff and Ord in 1974, which has proven useful in modelling the temporal aspects of spatially located data. This model can simulate the trends in HFRS epidemics, taking into consideration both spatial and temporal variations. The SD-STARIMA model is also able to make seasonal difference calculations to eliminate temporally non-stationary problems that are present in the HFRS data. Experiments have demonstrated that the proposed SD-STARIMA model offers notably better prediction accuracy, especially for spatiotemporal series data with seasonal distribution characteristics.

Pemodelan Harga Beras di Pulau Sumatera dengan Menggunakan Model Generalized Space Time ARIMA

Generalized space time autoregressive integrated moving average (GSTARIMA) model is a time series model of multiple variables with spatial and time linkages (space time). GSTARIMA model is an extension of the space time autoregressive integrated moving average (STARIMA) model with the assumption that each location has unique model parameters, thus GSTARIMA model is more flexible than STARIMA model. The purposes of this research are to determine the best model and predict the time series data of rice price on all provincial capitals of Sumatra island using GSTARIMA model. This research used weekly data of rice price on all provincial capitals of Sumatra island from January 2010 to December 2017. The spatial weights used in this research are the inverse distance and queen contiguity. The modeling result shows that the best model is GSTARIMA (1,1,0) with queen contiguity weighted matrix and has the smallest MAPE value of 1.17817 %.

Localized Space-Time Autoregressive Parameters Estimation for Traffic Flow Prediction in Urban Road Networks

With the rapid increase of private vehicles, traffic congestion has become a worldwide problem. Various models have been proposed to undertake traffic prediction. Among them, autoregressive integrated moving average (ARIMA) models are quite popular for their good performance (simple, low complexity, etc.) in traffic prediction. Localized Space-Time ARIMA (LSTARIMA) improves ARIMA’s prediction accuracy by extending the widely used STARIMA with a dynamic weight matrix. In this paper, a localized space-time autoregressive (LSTAR) model was proposed and a new parameters estimation method was formulated based on the LSTARIMA model to reduce computational complexity for real-time prediction purposes. Moreover, two theorems are given and verified for parameter estimation of our proposed LSTAR model. The simulation results showed that LSTAR provided better prediction accuracy when compared to other time series models such as Shift, autoregressive (AR), seasonal moving average (Seasonal MA), and Space-Time AR (STAR). We found that the prediction accuracy of LSTAR was a bit lower than the LSTARIMA model in the simulation results. However, the computational complexity of the LSTAR model was also lower than the LSTARIMA model. Therefore, there exists a tradeoff between the prediction accuracy and the computational complexity for the two models.

A stochastic analysis of highway capacity: Empirical evidence and implications

ABSTRACTThis paper presents a stochastic characterization of highway capacity and explores its implications on ramp metering control at the corridor level. The stochastic variation of highway capacity is captured through a Space–Time Autoregressive Integrated Moving Average (STARIMA) model. It is identified following a Seasonal STARIMA model (0, 0, 23) × (0, 1, 0)2, which indicates that the capacities of adjacent locations are spatially–temporally correlated. Hourly capacity patterns further verify the stochastic nature of highway capacity. The goal of this paper is to study (1) how to take advantage of the extra information, such as capacity variation, and (2) what benefits can be gained from stochastic capacity modeling. The implication of stochastic capacity is investigated through a ramp metering case study. A mean–standard deviation formulation of capacity is proposed to achieve the trade-off between traffic operation efficiency and robustness. Following that, a modified stochastic capacity-constraint ZONE ramp metering scheme embedded cell transmission model algorithm is introduced. The numerical experiment suggests that considering capacity variation information would alleviate the spillback effect and improve throughput. Monte Carlo simulation further supports this argument. This study helps verify and characterize the stochastic nature of capacity, validates the benefits of using capacity variation information, and thus enhances the necessity of implementing stochastic capacity in traffic operation.

A space–time delay neural network model for travel time prediction

Research on space–time modelling and forecasting has focused on integrating space–time autocorrelation into statistical models to increase the accuracy of forecasting. These models include space–time autoregressive integrated moving average (STARIMA) and its various extensions. However, they are inadequate for the cases when the correlation between data is dynamic and heterogeneous, such as traffic network data. The aim of the paper is to integrate spatial and temporal autocorrelations of road traffic network by developing a novel space–time delay neural network (STDNN) model that capture the autocorrelation locally and dynamically. Validation of the space–time delay neural network is carried out using real data from London road traffic network with 22 links by comparing benchmark models such as Naïve, ARIMA, and STARIMA models. Study results show that STDNN outperforms the Naïve, ARIMA, and STARIMA models in prediction accuracy and has considerable advantages in travel time prediction.

Predicting machined surface topography based on high definition metrology

This paper aims to predict the three-dimensional surface topography for future machined parts based on high definition metrology (HDM). HDM can measure the 3D topography of previously machined surfaces with high resolution and large field of view, containing rich spatial-temporal information of the machined surfaces. Therefore, a space-time autoregressive integrated moving average (STARIMA) model is adopted to describe the spatial-temporal characteristics and predict the future surface. The model was validated by an experiment on the engine block face milling process. The results show a good agreement between the predicted surface and the real surface with an average forecast error of 0.181 micrometer for an area with 80×80 sites. The proposed surface topography prediction method can be used for the early warning of surface quality deterioration and pre-control of the manufacturing process.

A Dynamic Spatial Weight Matrix and Localized Space–Time Autoregressive Integrated Moving Average for Network Modeling

Various statistical model specifications for describing spatiotemporal processes have been proposed over the years, including the space–time autoregressive integrated moving average (STARIMA) and its various extensions. These model specifications assume that the correlation in data can be adequately described by parameters that are globally fixed spatially and/or temporally. They are inadequate for cases in which the correlations among data are dynamic and heterogeneous, such as network data. The aim of this article is to describe autocorrelation in network data with a dynamic spatial weight matrix and a localized STARIMA model that captures the autocorrelation locally (heterogeneity) and dynamically (nonstationarity). The specification is tested with traffic data collected for central London. The result shows that the performance of estimation and prediction is improved compared with standard STARIMA models that are widely used for space–time modeling.En los últimos años, se han propuesto diversas especificaciones de modelado estadístico para describir procesos espacio‐temporales. Esto incluye el modelo espacio‐temporal autorregresivo integrado de media móvil (STARIMA) y sus varios derivados. Estas especificaciones de modelo asumen que la correlación de los datos puede ser adecuadamente descrita por parámetros que se fijan a nivel global en el espacio y/o tiempo. Dichos parámetros son inadecuados para los casos en los que las correlaciones entre los datos son dinámicas y heterogéneas, como en el contexto de los datos de la red. El objetivo de este artículo es describir la autocorrelación en los datos de red con una matriz de ponderación espacial dinámica y un modelo STARIMA localizado (LSTARIMA) que captura la autocorrelación local (heterogeneidad) de forma dinámica (no estacionariedad). La especificación del modelo es evaluada con datos de tráfico recolectados en el centro de Londres. Los resultados demuestran que los rendimientos de estimación y predicción mejoran con el método propuesto en comparación con los modelos STARIMA estándar que son ampliamente utilizados para el modelado de espacio‐temporal.通过设定多种统计模型来描述地理时空过程已提出多年，包括时空自回归移动平均(STARIMA)及其变形。此类模型通过假设数据相关性可由在时间域或者空间域上全局不变的参数加以充分描述。因此，上述模型不适用于具有动态或异质相关性的数据，如网络数据。本文试图采用一个动态空间权重矩阵与局部时空自回归移动平均(LSTARIMA)模型来描述数据的自相关程度，以此捕捉局域自相关(异质性)和动态自相关(非平稳性)。以伦敦市中心的交通数据作为模型的实证案例的测试结果显示，相对于广泛应用于时空过程分析的标准STARIMA模型，本文的模型在参数估计和预测性能上均有提升。

Forecasting Traffic Volume with Space-Time ARIMA Model

The paper proposes a space–time autoregressive integrated moving average (STARIMA) model to predict the traffic volume in urban areas. The methodological framework incorporates the historical traffic data and the spatial features of a road network. Moreover, the spatial characteristics in a way that reflects not only the distance but also the average travel speed on the links. In order to response the time-varying speed, six traffic modes are classified by level of service (LOS) which is updated in 5 minute interval. In the end, with the real traffic data in Beijing for experiments, the model achieves a very good accuracy on the 5 minute interval forecasting, it also provides a sufficient accuracy of 30 minute interval forecasting compared with ARIMA model.

Space–time modeling of traffic flow

This paper discusses the application of space–time autoregressive integrated moving average (STARIMA) methodology for representing traffic flow patterns. Traffic flow data are in the form of spatial time series and are collected at specific locations at constant intervals of time. Important spatial characteristics of the space–time process are incorporated in the STARIMA model through the use of weighting matrices estimated on the basis of the distances among the various locations where data are collected. These matrices distinguish the space–time approach from the vector autoregressive moving average (VARMA) methodology and enable the model builders to control the number of the parameters that have to be estimated. The proposed models can be used for short-term forecasting of space–time stationary traffic-flow processes and for assessing the impact of traffic-flow changes on other parts of the network. The three-stage iterative space–time model building procedure is illustrated using 7.5 min average traffic flow data for a set of 25 loop-detectors located at roads that direct to the centre of the city of Athens, Greece. Data for two months with different traffic-flow characteristics are modelled in order to determine the stability of the parameter estimation.

Forecasting Traffic Flow Conditions in an Urban Network: Comparison of Multivariate and Univariate Approaches

Several univariate and multivariate models have been proposed for performing short-term forecasting of traffic flow. Two different univariate [historical average and ARIMA (autoregressive integrated moving average)] and two multivariate [VARMA (vector autoregressive moving average) and STARIMA (space–time ARIMA)] models are presented and discussed. A comparison of the forecasting performance of these four models is undertaken with data sets from 25 loop detectors located in major arterials in the city of Athens, Greece. The variable under study is the relative velocity, which is the traffic volume divided by the road occupancy. Although the specification of the network’s neighborhood structure for the STARIMA model was relatively simple and can be further refined, the results obtained indicate a comparable forecasting performance for the ARIMA, VARMA, and STARIMA models. The historical average model could not cope with the variability of the data sets at hand.

Comparison of stochastic approaches to the transportation problem: a case study

The objective of this case study is to provide insight to practitioners about the methodology of using the space-time autoregressive integrated moving average (STARIMA) class of models to formulate stochastic demand of the transportation problem. While providing insight, two other methods-expected value (EV) and stochastic approximation (SA)-are also employed to formulate demand. A comparative evaluation of the methods using brewery data for the distribution of four products from five production plants to 64 distribution centers is presented. It is shown that the demand characterized by the STARIMA approach results in a lower total cost of transportation. This occurs because the STARIMA approach results in better forecasts. Based upon the case study, the cost analysis indicated that the STARIMA method when used without (with) updating resulted in a 9.49% (10.5%) increase in the Company's net profit as compared with the SA method. Similarly, the STARIMA approach when used without (with) updating resulted in an 11.36% (12.37%) increase in the net profit as compared with the EV method. For the STARIMA approach, computations for a large size problem are shown to be identical to those of the deterministic transportation problem given the demand forecasts. Extra computation effort for producing STARIMA forecasts are easily justified in terms of the increased profit margin.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SPACE‐TIME MODELING OF VECTOR HYDROLOGIC SEQUENCES1

Stochastic modeling of vector hydrologic sequences is examined with a general class of space‐time autoregressive integrated moving average (STARIMA) models. The models describe spatial and temporal autocorrelatjon, through dependent variables lagged both in space and time. The model structures incorporate a hierarchical ordering scheme to map the vector of observations into a network configuration. The neighboring structure used introduces a physical/geographical hierarchy to enable the model identification procedures to assist in determining appropriate correlative relationships. The three‐stage iterative space‐time model building procedure is illustrated using average monthly streamfiow data for a four‐station network of the Southeastern Hydropower System.